HELP PLEASE

[blondie10]

I am working on a college algebra assignment. The question is square root of x+2 minus x equals 0!! I do not want the answer just want to know how to work the problem!!

 

[Loren]

To solve an equation involving a radical expression, isolate the radical on one side of the equation with all rational expressions on the other side. Square both sides. If there is only one radical to start with, the new equation has no radicals. Solve for the unknown. Be sure to check your answer(s) because you may have introduced extraneous roots.
If there were more than one radical to start with, repeat the process until there are none.

 

[BigGlenntheHeavy]

\(\displaystyle \sqrt{x+2}-x = 0.\)

\(\displaystyle \sqrt{x+2} \ = \ x,\)

\(\displaystyle x+2 \ = \ x^2, \ squaring \ both \ sides.\)

\(\displaystyle x^2-x-2 \ = \ 0.\)

\(\displaystyle (x-2)(x+1) \ = \ 0, \ \implies \ x \ =2 \ or \ x \ = \ -1.\)

\(\displaystyle Check \ in \ original \ equation, \ mandatory: \ x \ = \ -1 \ \implies \ 2 \ = \ 0, \ I \ don't \ think \ so.\)

\(\displaystyle x \ = \ 2, \ 2-2 \ = \ 0, \ checks, \ hence \ only \ solution \ to \ equation \ is \ x \ = \ 2.\)